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Hele-Shaw type free boundary problems as nonlinear fractional heat equations

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FD2W01 - Deterministic and stochastic fractional differential equations and jump processes

We will discuss a few different recent works which allow to convert some free boundary flows similar to Help-Shaw (in both one and two phase situations) into a nonlinear fractional heat equation for the function whose graph represents the moving free boundary.  After the conversion to a nonlinear fractional heat equation, the tools of viscosity solutions and Krylov-Safonov theory become applicable to give different types of well-posedness and regularization results than appear with different methods that treat the free boundary in its original form.  As the one-phase case is relatively well understood, these techniques are more novel for the two-phase setting.  This involves joints works with Abedin, Chang Lara, and Guillen. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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